This study reports how the Differential Evolution (DE) algorithm performed on the test bed developed for the CEC05 contest for real parameter optimization. The test bed includes 25 scalable functions, many of which are both non-separable and highly multi-modal. Results include DE's performance on the 10 and 30-dimensional versions of each function.

Multimodal function optimization, where the aim is to locate more than one solution, has attracted growing interest especially in the evolutionary computing research community. To evaluate experimentally the strengths and weaknesses of multimodal optimization algorithms, it is important to use test functions representing different characteristics and various levels of difficulty. The available selection of multimodal test problems is, however, rather limited and no general framework exists. This paper describes an attempt to construct a software framework which includes a variety of easily tunable test functions. The aim is to provide a general and easily expandable environment for testing different methods of multimodal optimization. Several function families with different characteristics are included. The framework implements new parameterizable function families for generating desired landscapes. Additionally the framework implements a selection of well known test functions from the literature, which can be rotated and stretched. The software module can easily be imported to any optimization algorithm implementation compatible with the C programming language. As an application example, 8 optimization approaches are compared by their ability to locate several global optima over a set of 16 functions with different properties generated by the proposed module. The effects of function regularity, dimensionality and number of local optima on the performance of different algorithms are studied.

This paper benchmarks the scaling performance of two mutation-only Differential Evolution algorithms with the goal of discovering why large population sizes are often needed to support optimizations with small scale factors. The algorithms differ only in how the base vector is selected. We determined the computational efficiency of both base vector selection methods with a test bed consisting of three convex and one non-convex uni-modal functions. Our experiments revealed the best control parameter combinations and their dependence on the objective function's dimension. In addition, results demonstrate the extent to which stretching, rotating and making the objective function landscape non-convex impact the performance of the differential mutation operator.

A new mutation concept is proposed to generalize local selection based Differential Evolution algorithm to work in general multimodal problems. Three variations of the proposed method are compared with classic Differential Evolution algorithm using a set of five well known test functions and their variants. The general idea of the new mutation operation is to divide the mutation into two parts: the local and global mutation. The global mutation works as a migration operator allowing the algorithm perform global search efficiently, while the local mutation improves the efficiency of local search.The results show that the concept of global mutation is able to generalize the good performance of local selection based Differential Evolution from convex uni-modal functions to general nonconvex and multi-modal problems. Among the tested functions, the new method was able to outperform the classic Differential Evolution in all but one. A limited analysis of the effects of control parameters to the performance of the algorithm is also done.

Abstract. The topic of multimodal function optimization, where the aim is to locate more than one solution, has attracted a growing interest especially in the evolutionary computing research community. To experimentally evaluate the strengths and weaknesses of multimodal optimization algorithms, it is important to use test functions representing different characteristics and of various levels of difficulty. However, the available selection of multimodal test problems with multiple global optima is rather limited at the moment and no general framework exists. This paper describes our attempt in constructing a test function generator to allow the generation of easily tunable test functions. The aim is to provide a general and easily expandable environment for testing different methods of multimodal optimization. Several function families with different characteristics are included. The generator implements new parameterizable function families for generating desired landscapes and a selection of well known test functions from literature, which can be rotated and stretched. The module can be easily imported to any optimization algorithm implementation compatible with C programming language.